Motivation TFRs for normal dynamics TFRs for anomalous dynamics Summary Fluctuation relations for anomalous dynamics

Consider a particle system evolving from some initial state into a nonequilibrium steady state. Measure the probability distribution ρ(ξt) of entropy production ξt during time t: ln ρ(ξt) ρ(−ξt) = ξt transient fluctuation relation (TFR) Evans et al. (1993/94); Gallavotti, Cohen (1995) why important? Of very general validity and 1 generalizes the Second Law to small noneq. systems 2 yields nonlinear response relations 3 connection with fluctuation dissipation relations 4 can be checked by experiments (Wang et al., 2002) Fluctuation relations for anomalous dynamics Rainer Klages 2 Motivation TFRs for normal dynamics TFRs for anomalous dynamics Summary Fluctuation relation and the Second Law meaning of TFR in terms of Second Law: ξ ρ(ξ) t1 t2 t3 t tξt−ξ t t1 < t2 < t3 ρ(ξt) = ρ(−ξt)exp(ξt) ≥ ρ(−ξt) (ξt ≥ 0) ⇒ < ξt> ≥ 0 goal: sample specifically the tails of the pdf... Fluctuation relations for anomalous dynamics Rainer Klages 3 Motivation TFRs for normal dynamics TFRs for anomalous dynamics Summary Fluctuation relation and scaling I look at the pdf of the scaled variable ξ̃t = ξt < ξt> for eliminating the drift (Touchette, Cohen, 2009): ξ ρ(ξ) t1 t2 t